// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2017 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#ifndef EIGEN_SYMBOLIC_INDEX_H
#define EIGEN_SYMBOLIC_INDEX_H

namespace Eigen {

/** \namespace Eigen::symbolic
  * \ingroup Core_Module
  *
  * This namespace defines a set of classes and functions to build and evaluate symbolic expressions of scalar type Index.
  * Here is a simple example:
  *
  * \code
  * // First step, defines symbols:
  * struct x_tag {};  static const symbolic::SymbolExpr<x_tag> x;
  * struct y_tag {};  static const symbolic::SymbolExpr<y_tag> y;
  * struct z_tag {};  static const symbolic::SymbolExpr<z_tag> z;
  *
  * // Defines an expression:
  * auto expr = (x+3)/y+z;
  *
  * // And evaluate it: (c++14)
  * std::cout << expr.eval(x=6,y=3,z=-13) << "\n";
  *
  * // In c++98/11, only one symbol per expression is supported for now:
  * auto expr98 = (3-x)/2;
  * std::cout << expr98.eval(x=6) << "\n";
  * \endcode
  *
  * It is currently only used internally to define and manipulate the Eigen::last and Eigen::lastp1 symbols in Eigen::seq and Eigen::seqN.
  *
  */
namespace symbolic {

    template <typename Tag> class Symbol;
    template <typename Arg0> class NegateExpr;
    template <typename Arg1, typename Arg2> class AddExpr;
    template <typename Arg1, typename Arg2> class ProductExpr;
    template <typename Arg1, typename Arg2> class QuotientExpr;

    // A simple wrapper around an integral value to provide the eval method.
    // We could also use a free-function symbolic_eval...
    template <typename IndexType = Index> class ValueExpr
    {
    public:
        ValueExpr(IndexType val) : m_value(val) {}
        template <typename T> IndexType eval_impl(const T&) const { return m_value; }

    protected:
        IndexType m_value;
    };

    // Specialization for compile-time value,
    // It is similar to ValueExpr(N) but this version helps the compiler to generate better code.
    template <int N> class ValueExpr<internal::FixedInt<N>>
    {
    public:
        ValueExpr() {}
        template <typename T> EIGEN_CONSTEXPR Index eval_impl(const T&) const { return N; }
    };

    /** \class BaseExpr
  * \ingroup Core_Module
  * Common base class of any symbolic expressions
  */
    template <typename Derived> class BaseExpr
    {
    public:
        const Derived& derived() const { return *static_cast<const Derived*>(this); }

        /** Evaluate the expression given the \a values of the symbols.
    *
    * \param values defines the values of the symbols, it can either be a SymbolValue or a std::tuple of SymbolValue
    *               as constructed by SymbolExpr::operator= operator.
    *
    */
        template <typename T> Index eval(const T& values) const { return derived().eval_impl(values); }

#if EIGEN_HAS_CXX14
        template <typename... Types> Index eval(Types&&... values) const { return derived().eval_impl(std::make_tuple(values...)); }
#endif

        NegateExpr<Derived> operator-() const { return NegateExpr<Derived>(derived()); }

        AddExpr<Derived, ValueExpr<>> operator+(Index b) const { return AddExpr<Derived, ValueExpr<>>(derived(), b); }
        AddExpr<Derived, ValueExpr<>> operator-(Index a) const { return AddExpr<Derived, ValueExpr<>>(derived(), -a); }
        ProductExpr<Derived, ValueExpr<>> operator*(Index a) const { return ProductExpr<Derived, ValueExpr<>>(derived(), a); }
        QuotientExpr<Derived, ValueExpr<>> operator/(Index a) const { return QuotientExpr<Derived, ValueExpr<>>(derived(), a); }

        friend AddExpr<Derived, ValueExpr<>> operator+(Index a, const BaseExpr& b) { return AddExpr<Derived, ValueExpr<>>(b.derived(), a); }
        friend AddExpr<NegateExpr<Derived>, ValueExpr<>> operator-(Index a, const BaseExpr& b)
        {
            return AddExpr<NegateExpr<Derived>, ValueExpr<>>(-b.derived(), a);
        }
        friend ProductExpr<ValueExpr<>, Derived> operator*(Index a, const BaseExpr& b) { return ProductExpr<ValueExpr<>, Derived>(a, b.derived()); }
        friend QuotientExpr<ValueExpr<>, Derived> operator/(Index a, const BaseExpr& b) { return QuotientExpr<ValueExpr<>, Derived>(a, b.derived()); }

        template <int N> AddExpr<Derived, ValueExpr<internal::FixedInt<N>>> operator+(internal::FixedInt<N>) const
        {
            return AddExpr<Derived, ValueExpr<internal::FixedInt<N>>>(derived(), ValueExpr<internal::FixedInt<N>>());
        }
        template <int N> AddExpr<Derived, ValueExpr<internal::FixedInt<-N>>> operator-(internal::FixedInt<N>) const
        {
            return AddExpr<Derived, ValueExpr<internal::FixedInt<-N>>>(derived(), ValueExpr<internal::FixedInt<-N>>());
        }
        template <int N> ProductExpr<Derived, ValueExpr<internal::FixedInt<N>>> operator*(internal::FixedInt<N>)const
        {
            return ProductExpr<Derived, ValueExpr<internal::FixedInt<N>>>(derived(), ValueExpr<internal::FixedInt<N>>());
        }
        template <int N> QuotientExpr<Derived, ValueExpr<internal::FixedInt<N>>> operator/(internal::FixedInt<N>) const
        {
            return QuotientExpr<Derived, ValueExpr<internal::FixedInt<N>>>(derived(), ValueExpr<internal::FixedInt<N>>());
        }

        template <int N> friend AddExpr<Derived, ValueExpr<internal::FixedInt<N>>> operator+(internal::FixedInt<N>, const BaseExpr& b)
        {
            return AddExpr<Derived, ValueExpr<internal::FixedInt<N>>>(b.derived(), ValueExpr<internal::FixedInt<N>>());
        }
        template <int N> friend AddExpr<NegateExpr<Derived>, ValueExpr<internal::FixedInt<N>>> operator-(internal::FixedInt<N>, const BaseExpr& b)
        {
            return AddExpr<NegateExpr<Derived>, ValueExpr<internal::FixedInt<N>>>(-b.derived(), ValueExpr<internal::FixedInt<N>>());
        }
        template <int N> friend ProductExpr<ValueExpr<internal::FixedInt<N>>, Derived> operator*(internal::FixedInt<N>, const BaseExpr& b)
        {
            return ProductExpr<ValueExpr<internal::FixedInt<N>>, Derived>(ValueExpr<internal::FixedInt<N>>(), b.derived());
        }
        template <int N> friend QuotientExpr<ValueExpr<internal::FixedInt<N>>, Derived> operator/(internal::FixedInt<N>, const BaseExpr& b)
        {
            return QuotientExpr<ValueExpr<internal::FixedInt<N>>, Derived>(ValueExpr<internal::FixedInt<N>>(), b.derived());
        }

#if (!EIGEN_HAS_CXX14)
        template <int N> AddExpr<Derived, ValueExpr<internal::FixedInt<N>>> operator+(internal::FixedInt<N> (*)()) const
        {
            return AddExpr<Derived, ValueExpr<internal::FixedInt<N>>>(derived(), ValueExpr<internal::FixedInt<N>>());
        }
        template <int N> AddExpr<Derived, ValueExpr<internal::FixedInt<-N>>> operator-(internal::FixedInt<N> (*)()) const
        {
            return AddExpr<Derived, ValueExpr<internal::FixedInt<-N>>>(derived(), ValueExpr<internal::FixedInt<-N>>());
        }
        template <int N> ProductExpr<Derived, ValueExpr<internal::FixedInt<N>>> operator*(internal::FixedInt<N> (*)()) const
        {
            return ProductExpr<Derived, ValueExpr<internal::FixedInt<N>>>(derived(), ValueExpr<internal::FixedInt<N>>());
        }
        template <int N> QuotientExpr<Derived, ValueExpr<internal::FixedInt<N>>> operator/(internal::FixedInt<N> (*)()) const
        {
            return QuotientExpr<Derived, ValueExpr<internal::FixedInt<N>>>(derived(), ValueExpr<internal::FixedInt<N>>());
        }

        template <int N> friend AddExpr<Derived, ValueExpr<internal::FixedInt<N>>> operator+(internal::FixedInt<N> (*)(), const BaseExpr& b)
        {
            return AddExpr<Derived, ValueExpr<internal::FixedInt<N>>>(b.derived(), ValueExpr<internal::FixedInt<N>>());
        }
        template <int N> friend AddExpr<NegateExpr<Derived>, ValueExpr<internal::FixedInt<N>>> operator-(internal::FixedInt<N> (*)(), const BaseExpr& b)
        {
            return AddExpr<NegateExpr<Derived>, ValueExpr<internal::FixedInt<N>>>(-b.derived(), ValueExpr<internal::FixedInt<N>>());
        }
        template <int N> friend ProductExpr<ValueExpr<internal::FixedInt<N>>, Derived> operator*(internal::FixedInt<N> (*)(), const BaseExpr& b)
        {
            return ProductExpr<ValueExpr<internal::FixedInt<N>>, Derived>(ValueExpr<internal::FixedInt<N>>(), b.derived());
        }
        template <int N> friend QuotientExpr<ValueExpr<internal::FixedInt<N>>, Derived> operator/(internal::FixedInt<N> (*)(), const BaseExpr& b)
        {
            return QuotientExpr<ValueExpr<internal::FixedInt<N>>, Derived>(ValueExpr<internal::FixedInt<N>>(), b.derived());
        }
#endif

        template <typename OtherDerived> AddExpr<Derived, OtherDerived> operator+(const BaseExpr<OtherDerived>& b) const
        {
            return AddExpr<Derived, OtherDerived>(derived(), b.derived());
        }

        template <typename OtherDerived> AddExpr<Derived, NegateExpr<OtherDerived>> operator-(const BaseExpr<OtherDerived>& b) const
        {
            return AddExpr<Derived, NegateExpr<OtherDerived>>(derived(), -b.derived());
        }

        template <typename OtherDerived> ProductExpr<Derived, OtherDerived> operator*(const BaseExpr<OtherDerived>& b) const
        {
            return ProductExpr<Derived, OtherDerived>(derived(), b.derived());
        }

        template <typename OtherDerived> QuotientExpr<Derived, OtherDerived> operator/(const BaseExpr<OtherDerived>& b) const
        {
            return QuotientExpr<Derived, OtherDerived>(derived(), b.derived());
        }
    };

    template <typename T> struct is_symbolic
    {
        // BaseExpr has no conversion ctor, so we only have to check whether T can be statically cast to its base class BaseExpr<T>.
        enum
        {
            value = internal::is_convertible<T, BaseExpr<T>>::value
        };
    };

    /** Represents the actual value of a symbol identified by its tag
  *
  * It is the return type of SymbolValue::operator=, and most of the time this is only way it is used.
  */
    template <typename Tag> class SymbolValue
    {
    public:
        /** Default constructor from the value \a val */
        SymbolValue(Index val) : m_value(val) {}

        /** \returns the stored value of the symbol */
        Index value() const { return m_value; }

    protected:
        Index m_value;
    };

    /** Expression of a symbol uniquely identified by the template parameter type \c tag */
    template <typename tag> class SymbolExpr : public BaseExpr<SymbolExpr<tag>>
    {
    public:
        /** Alias to the template parameter \c tag */
        typedef tag Tag;

        SymbolExpr() {}

        /** Associate the value \a val to the given symbol \c *this, uniquely identified by its \c Tag.
    *
    * The returned object should be passed to ExprBase::eval() to evaluate a given expression with this specified runtime-time value.
    */
        SymbolValue<Tag> operator=(Index val) const { return SymbolValue<Tag>(val); }

        Index eval_impl(const SymbolValue<Tag>& values) const { return values.value(); }

#if EIGEN_HAS_CXX14
        // C++14 versions suitable for multiple symbols
        template <typename... Types> Index eval_impl(const std::tuple<Types...>& values) const { return std::get<SymbolValue<Tag>>(values).value(); }
#endif
    };

    template <typename Arg0> class NegateExpr : public BaseExpr<NegateExpr<Arg0>>
    {
    public:
        NegateExpr(const Arg0& arg0) : m_arg0(arg0) {}

        template <typename T> Index eval_impl(const T& values) const { return -m_arg0.eval_impl(values); }

    protected:
        Arg0 m_arg0;
    };

    template <typename Arg0, typename Arg1> class AddExpr : public BaseExpr<AddExpr<Arg0, Arg1>>
    {
    public:
        AddExpr(const Arg0& arg0, const Arg1& arg1) : m_arg0(arg0), m_arg1(arg1) {}

        template <typename T> Index eval_impl(const T& values) const { return m_arg0.eval_impl(values) + m_arg1.eval_impl(values); }

    protected:
        Arg0 m_arg0;
        Arg1 m_arg1;
    };

    template <typename Arg0, typename Arg1> class ProductExpr : public BaseExpr<ProductExpr<Arg0, Arg1>>
    {
    public:
        ProductExpr(const Arg0& arg0, const Arg1& arg1) : m_arg0(arg0), m_arg1(arg1) {}

        template <typename T> Index eval_impl(const T& values) const { return m_arg0.eval_impl(values) * m_arg1.eval_impl(values); }

    protected:
        Arg0 m_arg0;
        Arg1 m_arg1;
    };

    template <typename Arg0, typename Arg1> class QuotientExpr : public BaseExpr<QuotientExpr<Arg0, Arg1>>
    {
    public:
        QuotientExpr(const Arg0& arg0, const Arg1& arg1) : m_arg0(arg0), m_arg1(arg1) {}

        template <typename T> Index eval_impl(const T& values) const { return m_arg0.eval_impl(values) / m_arg1.eval_impl(values); }

    protected:
        Arg0 m_arg0;
        Arg1 m_arg1;
    };

}  // end namespace symbolic

}  // end namespace Eigen

#endif  // EIGEN_SYMBOLIC_INDEX_H
